Probability Essentials Challenge

Froggy Jumps

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Test your probability know-how in quick-fire questions.

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Yousef

United States

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Froggy Jumps Probability Essentials ChallengeOnline version Test your probability know-how in quick-fire questions. by Yousef 1 Name the three main ways to determine the probability of an event. a Classical, empirical (relative frequency), and subjective b Deterministic, anecdotal, and random 2 What is the sample space when flipping two coins? a {H, T} b {Heads, Tails} c {HH, HT, TH, TT} 3 State the Addition Rule for probability and why modify for non‑mutually exclusive events. a P(AorB)=P(A)×P(B) b P(AorB)=P(A)−P(B) c P(AorB)=P(A)+P(B)−P(AandB); subtract intersection when not mutually exclusive 4 If P(A)=0.45, what is P(A′) (the complement)? a 0.45 b 0.75 c 0.55 5 What is the smallest and largest possible probability value? a 0 to 1 b -1 to 1 c 0 to 100 6 Define mutually exclusive events. If A and B are mutually exclusive, what is P(A and B)? a P(A and B)=P(A) b P(A and B)=P(B) c P(A and B)=0 7 Define independent events. What must hold if A and B are independent? a P(A and B)=P(A)+P(B) b P(A and B)=P(A)P(B) c P(A or B)=P(A)P(B) 8 Are M (soccer) and F (football) mutually exclusive? Are they independent? a Not mutually exclusive; independence not guaranteed b Mutually exclusive and not independent c Mutually exclusive and independent 9 Given P(A)=0.3, P(B)=0.5, P(A and B)=0.15. Are A and B independent? a Cannot determine from given data b No, since 0.3×0.5≠0.15 c Yes, since 0.3×0.5=0.15 10 What is the formula for conditional probability P(A\|B)? a P(A\|B)=P(B\|A)×P(A) b P(A\|B)=P(A∩B)/P(B) c P(A\|B)=P(A)+P(B)

Froggy Jumps

Probability Essentials ChallengeOnline version

Test your probability know-how in quick-fire questions.

by Yousef

Name the three main ways to determine the probability of an event.

Classical, empirical (relative frequency), and subjective

Deterministic, anecdotal, and random

What is the sample space when flipping two coins?

{H, T}

{Heads, Tails}

{HH, HT, TH, TT}

State the Addition Rule for probability and why modify for non‑mutually exclusive events.

P(AorB)=P(A)×P(B)

P(AorB)=P(A)−P(B)

P(AorB)=P(A)+P(B)−P(AandB); subtract intersection when not mutually exclusive

If P(A)=0.45, what is P(A′) (the complement)?

0.45

0.75

0.55

What is the smallest and largest possible probability value?

0 to 1

-1 to 1

0 to 100

Define mutually exclusive events. If A and B are mutually exclusive, what is P(A and B)?

P(A and B)=P(A)

P(A and B)=P(B)

P(A and B)=0

Define independent events. What must hold if A and B are independent?

P(A and B)=P(A)+P(B)

P(A and B)=P(A)P(B)

P(A or B)=P(A)P(B)

Are M (soccer) and F (football) mutually exclusive? Are they independent?

Not mutually exclusive; independence not guaranteed

Mutually exclusive and not independent

Mutually exclusive and independent

Given P(A)=0.3, P(B)=0.5, P(A and B)=0.15. Are A and B independent?

Cannot determine from given data

No, since 0.3×0.5≠0.15

Yes, since 0.3×0.5=0.15

What is the formula for conditional probability P(A|B)?

P(A|B)=P(B|A)×P(A)

P(A|B)=P(A∩B)/P(B)

P(A|B)=P(A)+P(B)

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Probability Essentials Challenge

Froggy Jumps

About this activity

Created by

Download the paper version to play

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Probability Essentials ChallengeOnline version

by Yousef

Name the three main ways to determine the probability of an event.

What is the sample space when flipping two coins?

State the Addition Rule for probability and why modify for non‑mutually exclusive events.

If P(A)=0.45, what is P(A′) (the complement)?

What is the smallest and largest possible probability value?

Define mutually exclusive events. If A and B are mutually exclusive, what is P(A and B)?

Define independent events. What must hold if A and B are independent?

Are M (soccer) and F (football) mutually exclusive? Are they independent?

Given P(A)=0.3, P(B)=0.5, P(A and B)=0.15. Are A and B independent?

What is the formula for conditional probability P(A|B)?

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